TITLE: Canonical form of a general Bilinear Form
QUESTION [6 upvotes]: There is a simple canonical form of a symmetric and antisymmetric bilibear forms. Is there a canonical form for a general bilinear form?

REPLY [3 votes]: People in matrix analysis would call this a "canonical form under congruence". Take a look at http://arxiv.org/abs/0709.2473; the solution is stated there.